B-Mo I just wanted to jump in and say that my LO started off on 2 hrly feeds, gradually (very slowly) managed to go to 2.5 and finally up to 3hrs, but we never went up to a 4 hr EASY (not until solids started at 6 months, bottles then went to 4 hrs instead of 3hrs and this happened very naturally for him). You do need to go back to the doc about getting proper meds, but meanwhile I hope you can feel a little reassured that my LO still learned to sleep independently despite the reflux (silent reflux to begin with) and it is possible to run an EASY on 2 or 2.5 hr E if that's what your LO needs to feel comfortable.
If necessary keep a log of all your EASY times in the day so that you can run the right length A and the right length E. Times might clash a bit but you can't force a baby to sleep sooner than their full A time just to fit in with more regular Es and you can't stretch out the Es if it causes pain.
With the sleep training, as long as you are responding to your LOs needs for comfort when in pain etc then it is still possible to get a few naps or night sleeps in the cot and put down awake, this is the beginning of independence. The nights were always the easiest for me to put DS down awake because he was the most relaxed then so took his bottle really well (BT and DF were always the biggest feeds and least painful).
Try not to pat to wind as this can agitate the reflux. Instead rub upwards on LOs left hand side on the back, or you might find applying just a tiny bit of pressure under the left side ribs (where the tummy is) can bring up the wind (I think Tracy describes both of these methods in SOTBW) I found if LO was swaddled I could hold him upright (tummy to tummy) and give him a firm hug and this brought the wind right up. Also avoid pat/shush for the same reason. Try a still hand, or a gently rubbing hand, or firmish pressure with the hand (whatever you suits you and LO)...you can of course still 'shush' as that doesn't effect reflux

hth some as it can be tricky knowing what to do x